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Henryk Hudzik – vita et opera

Mieczysław MastyłoJulian Musielak — 2015

Commentationes Mathematicae

This article contains a short vita of Henryk Hudzik's as well as a non-exhaustive survey of his contribution to various areas of analysis. We focus on the theory of Orlicz−Sobolev spaces and the geometry of Banach spaces. We highlight criteria for some important geometric properties related to the metric fixed point theory in some classes of Banach lattices, including Orlicz and Orlicz−Lorentz spaces, but we do not forget Henryk Hudzik's contribution to nonlinear integral equations and partial differential...

Approximation by nonlinear integral operators in some modular function spaces

Carlo BardaroJulian MusielakGianluca Vinti — 1996

Annales Polonici Mathematici

Let G be a locally compact Hausdorff group with Haar measure, and let L⁰(G) be the space of extended real-valued measurable functions on G, finite a.e. Let ϱ and η be modulars on L⁰(G). The error of approximation ϱ(a(Tf - f)) of a function f ( L ( G ) ) ϱ + η D o m T is estimated, where ( T f ) ( s ) = G K ( t - s , f ( t ) ) d t and K satisfies a generalized Lipschitz condition with respect to the second variable.

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